Question

You have a 10cm piece of string.
Can you bend it into a different shape with an area of 2.25 square cm? What is the shape and what are its dimensions?

Answer 1

Given:

Length of the string = 10 cm

Area of the figure = 2.25 cm²

To Find:

The shape and its dimension

Solution:

Define x:

Let x be the length of the rectangle.

Find the breath in term of x:

Perimeter of a rectangle = 2 (Length + Breadth)

2( x + Breadth) = 10

x + Breadth = 5

Breadth = 5 - x

Solve x:

Given that the area is 2.25 cm²

x (5 - x) = 2.25

5x - x² = 2.25

x² - 5x + 2.25 = 0

00x² - 500x + 225 = 0

25 (2x - 9)(2x - 1) = 0

x = 9/2 or x = 1/2

Answer: The shape is a rectangle and the dimension is 9/2 cm by 1/2 cm

Answer 2

Answer:

$\implies$ the shape and it's dimensions = x = 9/2 or x = 1/2

$\large\underline\mathrm{Given:-}$

Length of the string = 10cm

$\implies$ Area of the figures = 2.25cm²

$\large\underline\mathrm{To \: find}$

the shape and its dimensions?

$\large\underline\mathrm{Solution}$

Let x be the length of the rectangle.

perimeter of a rectangle = 2(l × b)

$\implies$ 2(x + b) = 10

$\implies$ x + b = 1

$\implies$ b = 5 - x

$\large\underline\mathrm{Solution}$

Given that the area is 2.25cm²

$\implies$ x(5 + x) = 2.25

$\implies$ 5x - x² = 2.25

$\implies$ x² - 5x + 2.25 = 0

$\implies$ 25(2x - 9) + 50(2x - 9) = 0

$\implies$ x = 9/2 or x = 1/2